Walking Gait Generation with Foot Placement Control
for the HOAP-3 Humanoid Robot
Yazhou Huang, Robert Backman and Marcelo Kallmann
UCM School of Engineering Technical Report TR-2011-002
University of California, Merced
{yhuang6,rbackman,mkallmann}@ucmerced.edu
Abstract— While biology-inspired approaches for computing
walking gaits are often based on joint oscillators, whenever
precise control of feet placement is needed a more specific
approach based on explicit footstep control is usually employed.
This paper presents a simple hybrid approach based on a gait
generator procedure that generates a patterned walking gait
based on trajectories to be followed by the feet and the center
of mass of the robot. While the trajectories can be modulated
according to high-level parameters offering realtime control of
the produced gait, the trajectories can also be modified in order
to achieve precise foot placements. Robust balance is achieved
by integrating a reactive realtime module which adjusts the
overall posture of the robot according to the readings of the feet
pressure sensors. We apply our gait generation method to the
HOAP-3 humanoid platform and several results are presented.
I. I NTRODUCTION
Fig. 1.
Walking is a key capability of humanoid robots and at the
same time it is one of the most difficult motions to achieve
precise control.
This paper presents a hybrid approach for generating walking
gaits which is based on a pattern generator that precisely controls feet placement according to parameterized trajectories.
We apply our method to the HOAP-3 humanoid robot, which
is illustrated in Figure 1.
In order to maintain balance when executing the generated
gait in the robot, our method includes a reactive module
which adjusts the center of mass of the robot according to
the readings of the feet sensors in order to achieve robust
balance maintenance.
The effectiveness of our gait generator and balance maintenance methods is demonstrated with several videos which
show the humanoid robot successfully walking in different
situations, and in particular executing paths among obstacles.
II. R ELATED W ORK
Research on humanoid locomotion involves many challenging aspects and different approaches are available in the literature for the purpose of humanoid walking gait generation.
In general these approaches can be classified into three main
categories described below.
In the first category, a limited knowledge of the robot
dynamics is used, as for example: the location of the center
The HOAP-3 humanoid robot (left) and its virtual model (right).
of mass (CoM), and the total angular momentum. Since the
walking controller knows little about the system structure,
these approaches usually rely on a feedback control loop
such as the Inverted Pendulum Model [1] [5].
In contrast, a second category of methods can be identified
when precise knowledge of the robot dynamics is availble,
for example: the CoM, the Zero Moment Point (ZMP) and
inertia of each link of the robot, etc. The performance
of these methods will mainly rely on the accuracy of the
computational model [2][9] .
The third category is represented by Central Pattern Generators (CPG) which are essentially, in most of the cases,
neural networks consisting of various mathematical neuron
models. The parameters of the models are optimized with
multiple objectives, and the outputs of the neurons are
utilized as the target angles of corresponding joints [10]
[3] [4]. However, less attention has been given for pattern
generators addressing precise placement of each foot step
during walk generation, which is a critical aspect when
walking among obstacles, which is the typical scenario of
approaches based on foot stepping planning [8].
In this paper we present a walk gait generator for bipedal
humanoid robots with explicit feet and CoM trajectory
manipulation in order to achieve realtime parameterization
of the produced gait and at the same time precise foot
Fig. 2. The snapshots show results of the generated walking gait. The left foot end-effector (red) and the right one (green) follow a predefined curve
(Figure 3) to step forward. IK is applied for both end-effectors at every frame to either maintain CoM projection at the center of the supporting footplate,
or to shift CoM from one foot to the other. First row: starting from standing pose, shifting CoM projection (green line) to left foot center (single support),
making a step with right foot, shifting CoM from left foot to right foot. Second row: making a step with the left foot while maintaining the CoM on top
of the right foot center, then alternating the support foot in order to make the next step. The vertical blue line indicates the projection of the root joint of
the robot on the floor.
placements. Our method is based on executing trajectories
solved by a fast analytical Inverse Kinematics (IK) solution,
which was designed specifically for the HOAP-3 humanoid
robot.
Our approach offers several advantages, in particular precise
feet placement for the walk gait generation can be guaranteed
at the maximum level while balance is maintained by placing
the CoM floor projection at optimal locations at each frame.
As our method is still based on a gait generator we are
also able to parameterize the output with high-level intuitive
parameters such as: walk speed, step distance, turning angle,
step height, etc, that can continuously vary within certain
ranges, resulting in a fine control of each step. This precise
foot placement with high level steering control is ideal for
scenarios involving locomotion among obstacles.
III. WALKING G AIT G ENERATION
The walking gait generation can be decomposed into a start
phase, a walking phase and a return phase. The gait is
generated by explicitly moving three joints: the root joint,
the left foot, and the right foot. At each time step the left
and right feet are considered to be end-effectors to be solved
by the IK, while the desired location for the root joint can
be freely moved while the IK maintain the feet preciselly
attached to the floor.
Figure 2 illustrates the process: from the start pose (double
support mode), the root joint is first translated to the top of
the supporting foot until the CoM projection lies perfectly at
the center of the supporting footplate (single support). The
other foot is now free to make a step while maintaining the
CoM unchanged. Note that the CoM is constantly changing
while the robot is moving and that the CoM can not be
directly manipulated, but it can be indirectly controlled by
moving the root joint position, i.e. moving the root joint
to the desired CoM location minus the difference vector
between the root joint location and the CoM of the robot in
the previous timestep. In order to achieve precise control, the
generator applies the IK for a few iterations at each timestep
in order to get to a pose that best satisfies the CoM constraint.
When making a step, the foot end-effector follows a predefined curve (see Figure 3) that lifts the foot off the ground
and moves forward (also sideways if stepping with a turning
angle). The root joint is then maintained at the same hight,
and turns in the same way as the stepping foot but only for
half of the angle, see Figure 4. This increases the chances for
solving the IK problem due to the limited range of motion in
the leg joints of the HOAP-3 robot. The step length, turning
angle, foot lift height are among several parameters which
can be continuously controlled during the gait generation.
If the parameters change drastically so that the IK can not
solve for the produced trajectory due to reachability or joint
range limits constraints, the generator on the fly adjusts the
end-effectors until solutions can be found. This is usually
done by adding rotation increments to adjust the stepping
foot (the current end-effector) and also by translating it away
from the body so that it can be lifted higher (in the case of
not being reachable). If no IK solutions can found for the
each footplate, from which the Center of Pressure (CoP)
can be acquired and it is then used as feedback for on-line
adjustment of CoM offset. A generic proportional-derivative
feedback control of the offset vector is applied in order to
reduce the oscillation of CoP.
Fig. 3. Curves used by the walking gait generator: foot lift curve y =
1 − (2x − 1)4 , x ∈ [0, 1] (top), and the adjustment of the leg base during
single support (see Figure 6) y = 1/2sin(4t − π/2) + 1/2, t ∈ [0, 1]
(bottom).
The results of the balance control are shown in 5. As we can
clearly see, the CoP trajectories obtained with the walking
generator with the balance controller active have much less
variations than the curves obtained without using the balance
controller. Note that the shape of the curves exhibit a lot
of noise as they were reconstructed with the real readings
obtained from the pressure sensors, which are noisy and have
varying range of response. Nevertheless the improvement in
the trajectories can be clearly observed when the balance
controller is activated. In Figure 5 the robot performs about 8
steps going straight, and readings from the 8 pressure sensors
located at the bottom of the feet are used to reconstructed
the CoP trajectory.
given set of parameters, the parameters will still be limited
with the priority of maintaining balance.
The generator outputs one pose at each time interval, and it
sends it immediately to a low-level communication module.
The module interpolates from the current configuration of the
robot, which is received by a network connection at a fixed
frame rate (60 fps). See section VI for details. By varying
the time interval, turning angle and step length, the generator
can be easily be applied for applications such as footstep
placement for path following, or walking interactive control
from a joystick, etc.
IV. BALANCE C ONTROL
When the generated walking gaits are simply applied to
the robot with no further corrections, the robot is able to
walk however the balance is usually lost when the CoM
transition becomes too fast. We implemented two simple
controllers to solve the balance maintenance problem: leg
base tilt correction and CoM offset correction. The humanoid
looses balance during a fast gait mainly because it lacks a fast
response to translate the CoM before entering (and during)
a single support phase.
We apply an additional rotation for the supporting leg for
balance compensation, which largely follows the sinusoidal
curve shown in Figure 3-bottom. The x-axis is the time and
the y-axis is the magnitude of such compensation, which
makes the CoM projection overshoot over the desired target
and increase the transition speed. The magnitude of the
maximum overshoot angle and the parameters of this curve
were adjusted during several walking tests until a suitable
shape was obtained.
The CoM offset is a time-variant 2-D vector. It adds on top
of the supporting footplate center as the desired location of
the CoM projection, allowing subtle balance tuning during
single support phase. Four pressure sensors are located below
Fig. 5. Comparison of CoP trajectories with and without on-line adjustments: upper row: slow walk, lower row: fast walk; left column: without
adjustment, right column: with on-line adjustment, which obviously reduces
the oscillation
The results obtained with the balance controller greatly
improve the motion and clearly produce a much smoother
Fig. 4. Snapshots of making a right turn (bottom view). First row: starting from a standing posture, the CoM projection is shifted to the left footplate
center (single support), and a right-turn stepping with the right foot is made. The upper body only turns half of the angle. Second row: shifting the CoM
from the left foot to the right foot and then making a forward step with the left foot while maintaining the CoM on top of the right foot center and rotating
back the upper body.
and balanced walking motion, which is demonstrated in
examples with the robot which are available in the video
accompanying this paper.
Given an initial point pinit , a goal point pgoal , and a clearance distance r, the collision-free path P (pinit , pgoal , r) =
(p0 , p1 , . . . , pn ) is described as a polygonal line with vertices
pi , i ∈ {1, . . . , n}, describing the solution path. As the path
turns around obstacles with distance r from the obstacles,
every corner of the path is a circle arc which is approximated
with points, making sure that the polygonal approximation
remains of r clearance from the obstacles.
In order to compute P (pinit , pgoal , r), we have extended an
existing triangulation-based path finding method [6, 7] with
the capability of generating paths with guaranteed clearance
r from the obstacles. The original method is based on three
parts: first a constrained Delaunay triangulation is performed
for exactly describing the polygonal obstacles, then an A*
search over the adjacency graph connecting the free triangles
is performed until a sequence of triangles joining pinit and
pgoal is found, and finally the shortest path inside the triangle
sequence can be computed with a simple linear pass using
the funnnel algorithm.
Fig. 6.
support.
Adjustment is made to reduce lateral oscillation during single
V. F INDING PATHS WITH C LEARANCE
Our walking gait generator is suitable for precise walking
control and we present as example the use of a path planner to compute trajectories among obstacles which can be
executed by our walking controller.
In order to extend the method for computing paths with
r-clearance, several modifications to the main algorithm
were needed: 1) each expansion during the A* search was
extended to include tests for checking if the triangle being
expanded can be traversed by a disc of radius r without
collisions, 2) a triangle refinement procedure was also needed
in order to correctly handle all sizes and shapes of the
triangles being traversed, 3) the linear funnel pass described
in the original method [6, 7] was extended to work with
circles of radius r and several special cases happening at the
beginning and end of the path were also specifically tested
and handled. We omit details about these extensions since
their explanation are overly long and not directly related
to our present work on walking control. Our main purpose
here is to present that collision free paths with guaranteed
clearance r can be efficiently computed and are suitable for
executaion with the proposed walking gait generator.
Figure 7 shows a collision-free path and channel produced
by our method. The figure also shows the node expansions
performed during the search for the path. In this way we
perform the needed global search for a path very efficiently
in the triangulation, avoiding resolution-dependent methods
such as when using grid-based subdivisions. Note that the
number of vertices n for describing the polygonal obstacles is
much smaller than the number of cells needed in grid-based
representations, and this reduced number of cells employed
by our method makes our approach for path finding very
efficient.
is taken from the queue a data log is created that includes
the pressure sensors in the feet,accelerometers,gyros and the
corresponding encoder values. This information is then sent
back through the server to the user interface for display and
optimization.
There is also a separate computer which is dedicated to
tracking the robot and any obstacles. A separate server
is set up on this computer which enables retrieval of the
global position and orientation of the robot and the obstacles
any time that it is queried. With the combination of the
sensor data log from the robot and the global position and
orientation from the Tracking system an accurate depiction
of the robot and its environment can be made in real-time.
Fig. 8.
Overall system architecture for controlling the robot.
VII. R ESULTS
Fig. 7. The left image illustrates a computed collision-free path and channel
with given clearance radius. The right image shows the expanded nodes of
the A* search during the path computation.
VI. R EALTIME E XECUTION IN THE HOAP P LATFORM
There are mainly three components to the network interface
controlling the robot: a user interface client application, a
server application running on the robot’s on board computer,
and a real-time module that has dedicated access to the motor
control board.
The user interface is running on a dedicated computer, and
is where the motion is generated. For each frame of motion
the posture of the robot is converted from joint angles to
encoder values and is put into a message struct along with
the step size for the real-time module. The main method to
control the overall speed of the robot is by adjusting the step
size for each posture sent. The message is then sent over the
network to the server on the robotson board computer. When
the server receives a posture message from the UI it relays it
directly to the real-time module. When the real-time module
receives a message it places it into a circular queue. The
real-time module starts interpolating the postures and sends
each increment to the motor control board.
For each step the real-time module pulls a posture from the
queue along with the step size. The number of interpolation
steps is determined by the largest difference in motor positions between the current and next posture divided by the step
size. The increment for each motor is given by the difference
in position divided by the number of steps. This ensures that
for each move all of the motors start and end at the same time
and the overall motion is continuous. Each time a posture
Figure 9 illustrates the effectiveness of the reactive balance control applied in conjunction with the walking gait
generator. Figure 10 shows an example of a path planned
among obstacles which was computed by the described
triangulation-based decomposition planning approach. The
figure also shows several snapshots of the robot executing
the path among obstacles.
The path execution of Figure 9 is performed by adjusting in
realtime the gait generator parameters such that feet placements following the given path are achieved. The generated
walking gait is able to precisely execute the given path.
Our results indicate that the proposed overall approach for
walking generation is well suited for such types of tasks
requiring fine walking control.
VIII. C ONCLUSIONS AND F UTURE W ORK
This report describes a simple walking gait generator method
that generates parameterized walking gaits with precise feet
placements. We successfully applied our gait generation
method to the HOAP-3 humanoid platform and several
results were presented. As future work we intend to add dynamic balance mechanisms in order to improve the smoothness and reliability of the walking.
Acknowledgments: the presented work was partially funded
by NSF award BCS-0821766.
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